Improving stock assessments in Hawaiʻi

Objectives

  • Estimate abundance of rough-toothed dolphins in Kauaʻi
  • Estimate stock-level space use

Challenges

  • Sampling restricted by conditions
  • Dolphin movement appears less restricted
  • Non-systematic surveys, variable effort

Non-systematic photo-ID surveys

Telemetry data

Space-use covariate

Modeling Framework

  • Spatial capture-recapture (SCR) for photo-ID data
  • Resource selection function (RSF) for “geolocator data”
  • Integrate the two via Royle et al. (2013)

Spatial capture-recapture model

Density model \[ \mathbf{s}_i \sim \text{Uniform}(\mathcal{S}) \]

Photo-ID data

\[ y_{ij} \sim \text{Binomial}\left(T_j, \; 1 - \exp\left(-\lambda_{ij}\right)\right) \\ \]

Detection model

\[\begin{equation} \lambda_{ij} = \exp\left(\alpha_0 - \color{red}{\alpha_1} d_{ij}^2 + \color{blue}{\alpha_2} \text{depth}_j + \color{green}{\alpha_3} \text{depth}_j ^2\right) \\ ~ \\ d_{ij} = ||\mathbf{s}_i - \mathbf{r}_j|| \\ \end{equation}\]

Resource selection function

Telemetry data

\[ x_{mk} \sim \text{Multinomial}(R_m, \; \pi_{mk}) \]

Selection model

\[\begin{equation} \pi_{mk} = \frac{\exp(- \color{red}{\alpha_1} d_{mk}^2 + \color{blue}{\alpha_2} \text{depth}_k + \color{green}{\alpha_3} \text{depth}_k ^2)} {\sum_{k=1}^K \exp(- \color{red}{\alpha_1} d_{mk}^2 + \color{blue}{\alpha_2} \text{depth}_k + \color{green}{\alpha_3} \text{depth}_k ^2)} \\ ~ \\ d_{mk} = ||\mathbf{s}_m - \mathbf{z}_k|| \end{equation}\]

Sampling

Priors

\[\begin{equation} M = 3000 \\ \psi \sim \text{Uniform}(0, 1) \\ \alpha_0 \sim \text{Uniform}(-10, 10) \\ \alpha_1 = 1 / (2\sigma^2) \\ \sigma \sim \text{HalfNormal}(10) \\ \alpha_2 \sim \text{Normal}(0, 2) \\ \alpha_3 \sim \text{Normal}(0, 2) \\ \end{equation}\]

PyMC Settings

  • No U-turn Sampler
  • 8 chains
  • 2000 tuning samples (discarded)
  • 1000 post-tune samples

Results: Parameter estimates



Coefficients

Parameter Median 90% CI
\(\alpha_2\) 0.52 (0.42, 0.60)
\(\alpha_3\) -0.35 (-0.41, -0.29)
\(\alpha_0\) -5.79 (-5.91, -5.67)
\(\sigma\) 22.8 (21.9, 23.7)
\(\psi\) 0.51 (0.46, 0.56)

Results: Space-use

  • Predicts high use in channel (good)

Results: Space-use

  • Predicts high use in channel (good)
  • Also predicts high use in other areas (not so good)

Results: Abundance

Interpretation

  • First abundance estimate for the population
  • New baseline, if stock is broken up

Next steps: Location data

  • Model measurement error, or use newer deployments

Next steps: Stock complex

  • Other rough-toothed dolphin populations
  • Landscape connectivity SCR
  • Mixture SCR

\(s_{i,q=1} \sim \text{Normal}(\mathbf{\mu}_{q=1}, \sigma \mathbf{I})\) \(s_{i,q=2} \sim \text{Normal}(\mathbf{\mu}_{q=2}, \sigma \mathbf{I})\)

Next steps: Location data

  • Incorporate additional covariates
  • Second-order selection
  • Posterior predictive checks
  • Pacfic Missile Range Facility
  • Other stocks and landscape connectivity

Thank You

Questions?


Contact Information
pattonp@hawaii.edu
philpatton.github.io

References

Royle, J Andrew, Richard B Chandler, Catherine C Sun, and Angela K Fuller. 2013. “Integrating Resource Selection Information with Spatial Capture–Recapture.” Methods in Ecology and Evolution 4 (6): 520–30.